Generalized fuzzy c-shells clustering and detection of circular and elliptical boundaries

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The Fuzzy c-Shells (FCS) algorithm and its adaptive generalization, called the Adaptive Fuzzy c-Shells (AFCS) algorithm, are considered for detection of curved boundaries, specifically circular and elliptical. The FCS algorithms utilize hyper-spherical-shells as cluster prototypes. Thus in two dimensions, the prototypes are circles. The AFCS algorithms consider hyper-ellipsoidal-shells as prototypes, hence the ability to characterize elliptical boundaries. The generalization is achieved by allowing the distances to be measured through a norm inducing matrix that is symmetric, positive definite. Each cluster is allowed to have a different matrix, which is made a variable of optimization. The ability of the algorithms to detect circular and elliptical boundaries in two-dimensional data is illustrated through several examples.

Original languageEnglish (US)
Pages (from-to)713-721
Number of pages9
JournalPattern Recognition
Issue number7
StatePublished - Jul 1992

All Science Journal Classification (ASJC) codes

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence


  • Adaptive clustering
  • Circle detection
  • Cluster analysis
  • Ellipse detection
  • Fuzzy clustering
  • Hough transforms
  • Image processing
  • Pattern recognition

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